THEORY OF VIBRATION OF THE LARYNX 215 



- T- = - HA + h)- -^ — h -^-^ g^ + etc. • (15) 



dq2 ^ dq-i dq-r ) 



Again by neglecting second and higher order effects this reaction 

 becomes 



It will be seen that the first term of this expression represents a 

 static force tending, since it is negative, to draw the vocal cords 

 together. This is the BernoulU effect utilized in a venturi meter. 

 This steady force is counterbalanced by an elastic reaction of the vocal 

 cords with which it combines to determine an equilibrium position 

 which obtains when the cords are not vibrating. This term may, 

 therefore, be dropped from the fin'al equations representing only 

 superimposed motions. 



The coefficient of i] is identical, except for a sign, with G of (13). 

 It represents a force on the vocal cords due to a superimposed part 

 of the Bernoulli effect caused by the small superimposed velocity ix 

 in the glottis. The coefficient of qo is dimensionally a stiffness. This 

 apparent stiffness is due to the nature of the air flow and is inde- 

 pendent of any elastic members. It is negative if the second differ- 

 ential of glottis mass with respect to cord displacement is negative, 

 positive when this coefficient is positive and vanishes when this 

 coefficient is zero. It simply adds or subtracts in effect from the 

 stiffness K-i of the vocal cords. The first possibility is the more likely.^ 

 These terms may then be written for simplicity 



-^= - F - Gh - K^q,. (17) 



oq-i 



Force Equations of the Larynx 



The force equations of the glottis and vocal cords with constants 

 thus evaluated are 



E, = Lr^ + R,H + Gk + R,U + /v„?o, (18) 



= Lo^ + R^u + A>, + K.Q. - F - Gi, - K^q.,. (19) 



As explained before, Eq = i^o^i and F = KoQn; so these cancel and 

 are of no interest here. In the following it will be seen that the field 



^ This coefficient has since been found to be negative. 



